On the Dissipative Version of the Gross--Pitaevski Equation
K. Paw{\l}owski, {\L}. A. Turski
TL;DR
This paper introduces a new dissipative Gross--Pitaevski equation that conserves particle number, based on a metriplectic formulation, offering a novel approach to modeling dissipative quantum systems.
Contribution
It presents a novel dissipative Gross--Pitaevskii equation using metriplectic dynamics that uniquely conserves particle number, unlike previous models.
Findings
The new equation maintains particle number conservation.
The metriplectic formulation effectively models dissipative quantum systems.
The approach differs from previous dissipative models by ensuring conservation laws.
Abstract
We propose a novel version of the dissipative Gross--Pitaevski equation and examine its properties. In contrast to previous proposals our approach, based on the metriplectic formulation of the dissipative system dynamics, conserves the number of particles in the system.
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